Kant’s Treatment of the Mathematical Antinomies in the First Critique and in the Prolegomena: A Comparison
Kant’s Treatment of the Mathematical Antinomies in the First Critique and in the Prolegomena: A Comparison

Summary/Abstract: This paper deals with an apparent contradiction between Kant’s account and solution of the mathematical antinomies of pure speculative reason in the Critique of Pure Reason and in the Prolegomena. In the first Critique, Kant claims that the theses are affirmative judgments, of the form ‘A is B’, and the antitheses are infinite judgments, of the form ‘A is non-B’. The theses and the antitheses are contradictorily opposed (i.e., the one true and the other false) and their proofs are valid only if a certain condition takes places, that is, if the world has a determinate magnitude. Otherwise, both are false and their proofs are wrong. Given transcendental realism, this condition takes place and the mathematical antinomies arise. Given transcendental idealism, this condition does not take place, the theses and the antitheses are false, and the mathematical antinomies disappear. At a first glance, according to the Prolegomena the theses are affirmative judgments and the antitheses are not infinite judgments, but negative judgments, of the form ‘A is not B’. Transcendental idealism granted, the subject common to theses and antitheses, namely, the concept of ‘world’, is inconsistent. Both judgments are false by the rule ‘non entis nulla sunt praedicata’ and the antinomies do not take place. These accounts seem to be incompatible with each other. Are the antitheses infinite or negative judgments? Are the antinomies solved because the world does not have a determinate magnitude, or because its notion is inconsistent?

• Details
• Contents